On the determination of the optimal constant output feedback gains for linear multivariable systems
TL;DR: In this article, the optimal control of linear time-invariant systems with respect to a quadratic performance criterion is discussed and an algorithm for computing FAST is presented.
Abstract: The optimal control of linear time-invariant systems with respect to a quadratic performance criterion is discussed. The problem is posed with the additional constraint that the control vector u(t) is a linear time-invariant function of the output vector y(t) (u(t) = -Fy(t)) rather than of the state vector x(t) . The performance criterion is then averaged, and algebraic necessary conditions for a minimizing F\ast are found. In addition, an algorithm for computing F\ast is presented.
Citations
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TL;DR: Although many approaches and techniques exist to approach different versions of the static output feedback problem in the control of linear, time-invariant systems, no efficient algorithmic solutions are available.
952Â citations
Cites background from "On the determination of the optimal..."
...4) and their discrete counterparts were proposed in (Choi and Sirisena, 1974; Kreisselmeier, 1975; Levine and Athans, 1970; Moerder and Calise, 1985; O'Reilly, 1978; S oderstr om, 1978; Toivonen, 1985)....
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...In (Johnson and Athans, 1970; Levine and Athans, 1970; Levine et al., 1971; Moerder and Calise, 1985), necessary conditions for optimality were given as 0 = ATc S + SAc +Q CTKTRKC (0....
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...It is generally assumed that x(0) is uniformly distributed on the unit sphere so that X = I (Levine and Athans, 1970)....
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TL;DR: This paper presents a mathematical framework for discussion of large space structure (LSS) control theory, and current trends in LSS control theory and related topics in general control science are surveyed.
Abstract: This paper presents a mathematical framework for discussion of large space structure (LSS) control theory. Within this framework, current trends in LSS control theory and related topics in general control science are surveyed.
672Â citations
01 Dec 1976
TL;DR: Multi-loop linear-quadratic state-feedback regulators are shown to be robust against a variety of large dynamical, time-varying, and non-linear variations in open-loop dynamics, strengthening the link between classical and modern feed-back theory.
Abstract: Multiloop linear-quadratic state-feedback (LQSF) regulators are shown to be robust against a variety of large dynamical linear time-invariant and memoryless nonlinear time-varying variations in open-loop dynamics. The results are interpreted in terms of the classical concepts of gain and phase margin, thus strengthening the link between classical and modern feedback theory.
518Â citations
Cites background from "On the determination of the optimal..."
...Also there are interesting and as yet unresolved issues of the robustness properties of output (or limited-state) variable feedback designs using quadratic performance criteria [31]....
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Book•
01 Jan 1992
TL;DR: A survey of the results and open problems in feedback control of large-scale systems of multivariable feedback systems and structure of interconnected systems.
Abstract: Large scale control systems results of multivariable feedback systems models and structure of interconnected systems decentralized stabilizability the decentralized stabilization and pole assignment optimal decentralized control stability analysis of interconnected systems decentralized design for strongly coupled subsystems decentralized design for weakly coupled systems decentralized PI controllers strongly coupled symmetric composite systems survey of the results and open problems in feedback control of large-scale systems.
427Â citations
14 Dec 1994
TL;DR: In this paper, the static output feedback problem in the control of linear, time-invariant (LTI) systems is reviewed and the knowledge gained in the decades of research into this most important problem is presented.
Abstract: This paper reviews the static output feedback problem in the control of linear, time-invariant (LTI) systems. It includes analytical and computational methods and presents in a unified fashion, the knowledge gained in the decades of research into this most important problem. >
414Â citations
Cites background or methods from "On the determination of the optimal..."
...A related algorithm was given in Miminis (1985) to assign max (m, p) poles....
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...It is generally assumed that x(O) is uniformly distributed on the unit sphere, so that X = I (Levine and Athans, 1970)....
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References
More filters
TL;DR: The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results and properties of the variance equation are of great interest in the theory of adaptive systems.
Abstract: A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this \"variance equation\" completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side. Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.
6,152Â citations
TL;DR: In this article, it was shown that the design of an observer for a system with M outputs can be reduced to the design for m separate observers for single-output subsystems.
Abstract: Often in control design it is necessary to construct estimates of state variables which are not available by direct measurement. If a system is linear, its state vector can be approximately reconstructed by building an observer which is itself a linear system driven by the available outputs and inputs of the original system. The state vector of an n th order system with m independent outputs can be reconstructed with an observer of order n-m . In this paper it is shown that the design of an observer for a system with M outputs can be reduced to the design of m separate observers for single-output subsystems. This result is a consequence of a special canonical form developed in the paper for multiple-output systems. In the special case of reconstruction of a single linear functional of the unknown state vector, it is shown that a great reduction in observer complexity is often possible. Finally, the application of observers to control design is investigated. It is shown that an observer's estimate of the system state vector can be used in place of the actual state vector in linear or nonlinear feedback designs without loss of stability.
1,611Â citations
TL;DR: The theory and the computational algorithm required to determine the piecewise-constant feedback gains for the optimal control of a linear system with quadratic performance index over a finite control interval is presented.
Abstract: This paper presents the theory and the computational algorithm required to determine the piecewise-constant feedback gains for the optimal control of a linear system with quadratic performance index over a finite control interval [t_{0} T] . A third order example illustrates the relation of the piecewise-constant gains to the truly optimal time-varying gains.
87Â citations
01 Jan 1968
TL;DR: Optimal control of linear systems with state variables generated by linear feedback from output variables, considering time variance, is discussed in this paper. But it does not consider the time variance of the output variables.
Abstract: Optimal control of linear systems with state variables generated by linear feedback from output variables, considering time variance
17Â citations
4Â citations